FIG. 1 shows a conventional Francis hydraulic turbine 1 configured to convert hydraulic energy to torque to drive an electrical generator (not shown). Water typically flows through a spiral casing 2 into a distributor 13 surrounding a rotating runner 3 of the turbine 1. The distributor 13 may have stay vanes 132 and guide vanes 130. Water flows inward into the runner in a generally spiraling motion along a horizontal direction inside a turbine having a vertical axis. The rotational velocity of the water drives the runner to turn around the axis. As the water flows through the runner, the transport component of the water is turned from a horizontal flow to a generally vertical outflow. From the runner, water flows into a vertical cone of the draft tube 5 below the runner.
In the case of a turbine having a horizontal axis, the water flows inward into the runner in a generally spiraling motion. The rotational velocity of the water drives the runner to turn around the axis. As the water flows through the runner, the water is turned to a generally horizontal outflow. From the runner, water flows into a horizontal cone of the draft tube downstream from the runner.
The runner 3 of a Francis turbine typically includes a crown 6 having a surface of revolution extending towards the band 8 along an axis 11 of the runner 3, and blades 7 extending out from the surface of revolution of the crown 6 to an annular band 8. Each blade 7 has a leading edge and a trailing edge. The ends of these edges are joined to the crown 6 and the band 8. The runner 3 may be located above a bottom ring 22 in the turbine.
Water enters the runner 3, flows around the leading edges of the blades, flows between the blades, and passes over the trailing edges of the blades, then flows into the draft tube 5.
The velocity of the water is generally faster near the band than near the crown in the runner. The high velocity water flow results in relatively high hydraulic friction at and near the band which reduces the efficiency of the turbine, as part of the energy is lost to friction. The high velocity water also causes low static pressure in the runner. The low pressure can cause the formation of cavitation bubbles that can damage the surfaces of the blades, the band, and the crown.
In the field of water turbines, the runner band is also known as a shroud or ring. The crown is also known as a hub. The leading edge of a blade is also known as an inlet edge or an inflow edge. The trailing edge of a blade is also known as an outlet edge or an outflow edge of a runner blade. This disclosure may use the terms interchangeably in reference to the different runner components.
FIGS. 2 and 3 are side and bottom views, respectively, of an exemplary conventional Francis turbine runner 9 that rotates in direction (R) around a rotational axis 11 of the runner 9. The runner 9 includes an annular array of runner blades 10, an annular band 12, and a crown 14. The runner 9 rotates clockwise when viewed from the crown 14. The crown 14 has a surface of revolution that typically faces the band 12 along the rotational axis 11. An opening 23 in the crown 14 is coaxial with the axis 11, and may receive a shaft for a generator.
FIG. 2 shows the ends 18 of the blades 10 superimposed on the band 12 for purposes of illustration. The ends of the blades 10 are joined, e.g., welded, to the band 12, but need not extend through the band 12. The ends 18 of the blades 10 may not be visible through the band 12 in a practical embodiment of the runner 9.
The blades 10 are arranged in an annular array between the band 12 and crown 14 of the runner 9. The blades 10 direct water from the spiral casing 2 to flow between the band and the crown and into the draft tube 5 as shown in FIG. 1.
Each blade 10 has a similar shape extending as a curve from the leading edge 16 to the trailing edge 20. The leading edge 16 is at the inlet to the runner 9 and the trailing edge 20 is at the outlet. Pseudo-streamlines 17, 19 are drawn on the image of the blades 10 to illustrate the shape of the blades 10. Solid pseudo-streamlines 17 are shown on the suction side of the blades 10, and dashed pseudo-streamlines 19 are shown on the pressure side of the blades 10. The suction sides of the blades 10 face towards the rotation (R) direction of the runner, and the pressure sides face away from the rotation (R) direction. Each pseudo-streamline 17, 19 is drawn on the surface of the blade 10 from the leading edge 16 to a trailing edge 20.
Each blade 10 has four corners P, Q, S and T. Two corners P and S of blade end 21 abut the crown 14 and two corners Q and T abut the band 12. The corners P, S abut the outer surface of the crown 14. The corner P is near the upstream region of the crown 14 and the corner S is at the downstream region 25 of the crown 14. The corners Q and T of the blade end 18 abut the band 12, with corner Q being located close to a first rim of the band 12 and corner T being near a second rim of the band 12.
The outer surface of the crown 14 supports the ends 21 of the blades 10. The ends 21 may be joined to the crown such as by welding. The crown 14 may have an internal opening to receive a drive shaft. A portion 24 of the outer surface of the crown 14 extends beyond the corners S of the blades 10 in streamwise direction. The portion 24 of the crown 14 faces the draft tube 5.
The band 12 is an annular structure supporting the ends 18 of the blades 10. The band 12 may have a curvature that curves towards the axis 11 of the turbine runner 3. The curvature conforms to the edges 18 of the blades 10. The band has a length (L) and a diameter (D). Length (L) is a distance measured between the bottom 15 of the distributor 13 to the trailing edge T at the band 8. Diameter (D) is an outlet diameter of the runner 3, which is a diameter of the band 12 at the junction with the trailing edge T. A normalized band length, called a “band length ratio” in the context of this disclosure, may be characterized by the ratio of its length to its minimum diameter (L/D).
Conventional runners have a band length ratio of at least 17% (0.17). These are referred to as long runners in the context of this application.
In the context of this application, runners referred to as short runners have a band length ratio of less than 17% (0.17). Short runners have been tried in the past, but suffered from severe cavitation damages which damaged the runner and reduced its hydraulic efficiency. Cavitation is usually less excessive in long band runners with long blades. Conventional wisdom is that bands and blades should be long to avoid cavitation.
The increased length of the blades and the band in a long runner increases the mass of the runner. The hydraulic efficiency of the long runner suffers because of the increase in hydraulic frictional losses due to the increased wetted surface areas of the longer blades and band. Efforts to reduce cavitation in a runner and otherwise improve runner performance are disclosed in U.S. Pat. Nos. 6,135,716 and 4,479,757. There remains a need to improve runner performance and reduce cavitation in a runner.